Underground drilling, such as gas, oil, or geothermal drilling, generally involves drilling a bore through a formation deep in the earth. Such bores are formed by connecting a drill bit to long sections of pipe, referred to as a “drill pipe,” so as to form an assembly commonly referred to as a “drill string.” The drill string extends from the surface to the bottom of the bore. The drill bit is rotated so that the drill bit advances into the earth, thereby forming the bore. In rotary drilling, the drill bit is rotated by rotating the drill string at the surface. Pumps at the surface pump high-pressure drilling mud through an internal passage in the drill string and out through the drill bit. The drilling mud lubricates the drill bit, and flushes cuttings from the path of the drill bit. In some cases, the flowing mud also powers a drilling motor, commonly referred to as a “mud motor,” which turns the bit. In any event, the drilling mud flows back to the surface through an annular passage formed between the drill string and the surface of the bore. In general, optimal drilling is obtained when the rate of penetration of the drill bit into the formation is as high as possible while a vibration of drilling system is as low as possible. The rate of penetration (“ROP”) is a function of a number of variables, including the rotational speed of the drill bit and the weight-on-bit (“WOB”). The drilling environment, and especially hard rock drilling, can induce substantial vibration and shock into the drill string, which has an adverse impact of drilling performance.
Vibration is introduced by rotation of the drill bit, the motors used to rotate the drill bit, the pumping of drilling mud, imbalance in the drill string, etc. Vibration can cause premature failure of the various components of the drill string, premature dulling of the drill bit, or may cause the catastrophic failures of drilling system components. Drill string vibration includes axial vibration, lateral vibration and torsional vibration. “Axial vibration” refers to vibration in the direction along the drill string axis. “Lateral vibration” refers to vibration perpendicular to the drill string axis. Lateral vibration often arises because the drill string rotates in a bent condition. Two other sources of lateral vibration are “forward” and “backward”, or “reverse”, whirl. “Whirl” refers to a situation in which the bit orbits around the borehole in addition to rotating about its own axis. In backward whirl, the bit orbits in a direction opposite to the direction of rotation of the drill bit. “Torsional vibration,” also of concern in underground drilling, is usually the result of what is referred to as “stick-slip.” Stick-slip occurs when the drill bit or lower section of the drill string momentarily stops rotating (i.e., “sticks”) while the drill string above continues to rotate, thereby causing the drill string to “wind up,” after which the stuck element “slips” and rotates again. Often, the bit will over-speed as it unwinds.
Various system can be used to obtain and process information concerning a drilling operation, which can help improve drilling efficiency. Systems have been developed that can receive and process information from sensors near the drill bit and then transmit that information to surface equipment. Other systems can determine vibration of the bottomhole assembly, either downhole during a drill run, or at the surface. Many of such systems use finite element and/or finite difference techniques to assist in in analysis of drilling data, including vibration information.